Po přestávce budeme pokračovat.

Because po here requires the locative case when it means after in a time expression.

The basic dictionary form is přestávka = break.
After po, it changes to the locative singular:

• přestávka → po přestávce

This is why the ending changes from -ka to -ce.

In this sentence, po takes the locative.

So:

• po přestávce = after the break

This is a very common pattern in Czech:

• po obědě = after lunch
• po práci = after work
• po hodině = after the lesson / after an hour, depending on context

Be aware that po can have other meanings too, but with time expressions like this, it commonly means after and uses the locative.

Because pokračovat is an imperfective verb, and the normal future of imperfective verbs in Czech is formed with:

• a future form of být = to be
• plus the infinitive

So:

• budu pokračovat = I will continue
• budeš pokračovat = you will continue
• budeme pokračovat = we will continue

This is different from many perfective verbs, whose present forms often have future meaning.

Budeme is the 1st person plural future form of být = to be.

It means we will be, but in sentences like this it helps build the future tense:

• budeme pokračovat = we will continue

So the sentence structure is basically:

• Po přestávce = after the break
• budeme pokračovat = we will continue

Budeme pokračovat is enough.

In Czech, the verb ending already tells you the subject:

• budeme = we will

So the pronoun my = we is usually omitted unless you want emphasis or contrast.

For example:

• Budeme pokračovat. = We will continue.
• My budeme pokračovat, ale oni odejdou. = We will continue, but they will leave.

Yes, you could also say Budeme pokračovat po přestávce.

Both are grammatical:

• Po přestávce budeme pokračovat.
• Budeme pokračovat po přestávce.

The difference is mostly about focus and style:

• Po přestávce budeme pokračovat. puts the time expression first, often sounding natural when setting the scene.
• Budeme pokračovat po přestávce. starts with the action itself.

Czech word order is more flexible than English, but it is not random. It often reflects what is already known and what is being emphasized.

Because Czech does not have articles like a or the.

So Czech often expresses ideas that English needs articles for without adding any separate word:

• po přestávce = after the break / after a break

Which English article fits depends on the context, not on a separate Czech word.

The difficult part for many English speakers is ř in přestávce.

A rough pronunciation guide for the whole sentence is:

• Po přestávce budeme pokračovat
• approximately: po przhestahft-seh boo-deh-meh po-kra-cho-vat

A few notes:

• ř is a special Czech sound, something like a blend of r and zh.
• č in pokračovat sounds like ch in church.
• á is a long vowel, so přestávka has a long a sound.

You do not need perfect ř immediately; Czech speakers are very used to learners struggling with it.

Pokračovat means to continue, and it is an imperfective verb.

That means it describes an ongoing process or continuation rather than a completed whole. Because of that, its future is formed with budu / budeš / bude / budeme... + infinitive:

• budu pokračovat
• budeme pokračovat

This fits the meaning well, because continuing is naturally an ongoing action.

Yes. Po has several meanings in Czech depending on context.

Some common ones are:

• after → po přestávce = after the break
• along / on / over in some expressions
• for in some distributive expressions, such as po jednom = one by one

So you should not think of po as having only one fixed English translation. In this sentence, though, after is definitely the correct meaning.