Cum senatores inter se disputarent, tribunus suadebat ut ad bonum commune potius quam ad commodum privatum spectarent.

Here cum introduces a circumstantial clause: while / when the senators were debating among themselves.

In this kind of past narrative clause, Latin very often uses cum + subjunctive, not the indicative. So:

• cum ... disputarent = while / when ... were debating

The imperfect subjunctive fits the background setting of the sentence. It gives the sense of an ongoing situation in the past, within which the main action happened.

So this is not mainly a condition or a wish; it is a standard narrative use of cum.

Inter se means among themselves or with one another.

• inter = among / between
• se = themselves

Together, they show a reciprocal idea: the senators were debating with each other, not just speaking in general.

This is a very common Latin expression:

• inter se pugnant = they fight among themselves
• inter se loquuntur = they speak with one another

It is imperfect subjunctive for two reasons:

1. It is in a cum-clause of past narration.
2. The action is ongoing in the past.

So disputarent means something like:

• were debating
• kept debating

The imperfect here gives background action. The idea is not a single completed debate, but an action in progress while the tribune was urging something.

Suadebat is imperfect because it describes an action in progress or repeated in the past:

• the tribune was advising
• the tribune kept urging

This matches the imperfect in disputarent nicely. The whole sentence paints a scene in progress:

• the senators were debating
• the tribune was urging

Latin often uses the imperfect in this way for backgrounded or continuing past actions.

After verbs of advising, persuading, urging, or requesting, Latin often uses ut plus the subjunctive to express what someone is being urged to do.

So:

• suadebat ut ... spectarent = he was advising / urging that they should look to...

This construction is often called a substantive clause of purpose or, in many classroom grammars, an indirect command-like construction after verbs such as suadeo.

A useful point: with suadeo, Latin often has

• the person advised in the dative
• the action in an ut-clause

For example:

• eis suadet ut veniant = he advises them to come

In your sentence, the people being advised are understood from context: the senators.

Spectarent is subjunctive because it is inside the ut-clause after suadebat.

It is imperfect subjunctive because the main verb is a past tense (suadebat), so Latin normally follows the sequence of tenses:

• primary sequence: present/future main verb → usually present/perfect subjunctive
• secondary sequence: past main verb → usually imperfect/pluperfect subjunctive

Here:

• suadebat = past
• so spectarent = imperfect subjunctive

In sense, it means:

• he was urging them to look / have regard to

Literally, spectare can mean to look at or to watch, but here it has a more figurative meaning.

spectare ad often means:

• to look to
• to aim at
• to have regard for
• to consider

So:

• ad bonum commune spectarent = they should look to / have regard for the common good
• not just physically look at it

This is a very natural Latin way to express directing attention or policy toward a goal or principle.

They are accusative because they follow the preposition ad, which takes the accusative.

So:

• ad bonum commune
• ad commodum privatum

Both phrases depend on spectarent:

• to look to the common good
• rather than to private advantage

Also note the agreement:

• bonum and commune both modify the same idea and are accusative singular neuter
• commodum and privatum are also accusative singular neuter

Potius quam means rather than.

It sets up a contrast between two alternatives:

• ad bonum commune
• quam ad commodum privatum

So the tribune was urging them to direct their attention:

• rather to the common good
• than to private advantage

The word potius strengthens the comparison:

• more preferably
• rather

This is a very common Latin way to express preference.

Latin often leaves out subject pronouns when the verb ending already shows the person and number.

Here spectarent has the ending -rent, which tells you it is:

• third person plural

So the subject is understood as they. From the context, that means the senators.

Latin does this constantly:

• veniunt = they come
• dixit = he/she said

An explicit pronoun is usually added only for emphasis or contrast.

Yes, the word order is quite normal for Latin, even though it is more flexible than English.

The sentence is arranged roughly like this:

• Cum senatores inter se disputarent
  background clause first: while the senators were debating among themselves
• tribunus suadebat
  main clause: the tribune was urging
• ut ad bonum commune potius quam ad commodum privatum spectarent
  content of the urging: that they should look to the common good rather than private advantage

Latin often places:

• the background clause first
• the main verb later
• the ut-clause after verbs like suadebat

Also, the contrast is neatly highlighted by putting the two ad phrases in parallel:

• ad bonum commune
• ad commodum privatum

That parallelism makes the opposition very clear.