Sözleşme şartlarını müşterilerle müzakere etmeliyiz.

şart means “term” or “condition.”
-lar marks the plural (terms).
-ı is the definite direct object suffix (accusative).
So şartlarını = “the terms” as the object of the sentence.

Turkish allows noun–noun compounds directly.
sözleşme şartları literally “contract terms.”
You could also say sözleşmenin şartları (“the contract’s terms”)—both are correct and interchangeable in this context.

The suffix -le is the comitative/instrumental case meaning “with.”
So müşterilerle = “with clients.”
You may also hear müşterilerle birlikte or müşterilerle beraber for “together with clients.”

müzakere on its own is a noun meaning “negotiation.”
To turn it into a verb “to negotiate,” Turkish uses etmek (“to do”) after many loan-nouns.
Hence müzakere etmek = “to carry out a negotiation” = “to negotiate.”

The suffix -meli expresses necessity or obligation (“must/should”).
The ending -yiz marks 1st person plural (“we”).
So etmeliyiz = “we must/should do.”

müzakere edeceğiz uses the future tense suffix -ecek + iz = “we will negotiate.”
It states a simple future action.
By contrast, etmeliyiz conveys obligation (“we should negotiate”), not just a future plan.

Turkish follows a Subject–Object–Verb (SOV) order.
Even though biz (“we”) isn’t written, the verb etmeliyiz comes last as per that rule.

Turkish is a pro-drop language.
Verb endings (here -yiz in etmeliyiz) reveal the subject, so explicit pronouns like biz are often left out.