… suche zu meinem Vertragsende …
The preposition zu is correct here. The phrase zu einem gewissen Zeitpunkt is used to say that something that you are looking for starts at a certain point in time, in your example, when the contract ends.
… suche ab / nach meinem Vertragsende …
The prepositions ab and nach are actually not correct here. This phrase does not mean that you are (currently) looking for something that starts when the contract ends, but that the search itself starts when the contract ends. You can see this more easily by changing the word order:
Ich suche nach meinem Vertragsende nach irgendwas …
→ When will you look for something? When the contract ends.
Therefore, except for the preposition in, which should be im, your sentence is correct:
Momentan warte ich auf die Benotung meiner Masterarbeit und suche zu meinem Vertragsende inim August nach einer neuen Tätigkeit …