Learn Croatian: Vidim bivšeg klijenta tamo. - I see the former client there.

Because it is the direct object of the verb vidim (I see), which means it must be in the accusative case. For masculine nouns that represent living beings, we add an -a in the accusative. If the noun were an inanimate object, it would not change from its dictionary form.

Why does the adjective change to bivšeg?

Adjectives must match the noun they describe in gender, number, and case. Since klijenta is a masculine, animate noun in the accusative case, the adjective meaning former also takes a special accusative animate ending.

Why does bivšeg end in -eg instead of the usual -og?

This is due to the letter right before the ending. In Croatian, if an adjective's base ends in a soft consonant like š, č, ć, j, or ž, the ending changes from -og to -eg. Because bivši has that soft š, it becomes bivšeg.

Where is the word for I in this sentence?

Croatian usually drops subject pronouns like ja because the verb ending already tells us who is doing the action. The -m at the end of vidim means I see, so adding the pronoun is not needed unless you want to add special emphasis.