Learn Russian: Тебе часто удаётся уговорить клиентов?

The verb удаваться / удаться (to manage / to succeed) is an impersonal verb. In Russian, the person who succeeds is treated as the recipient of the success, so they must be in the Dative case. Here, the nominative ты becomes the dative тебе (literally meaning "to you it succeeds").

Why is удаётся in the imperfective aspect while уговорить is in the perfective aspect?

The word часто (often) tells us the attempt is a repeated, ongoing action, so the main verb удаётся must be imperfective. However, the action of persuading the clients is focused on the successful result of each of those attempts, so the infinitive уговорить (to successfully persuade) stays perfective.

Why does клиентов end in -ов? Isn't it the direct object of the verb?

It is the direct object, which means it is in the Accusative case. But because клиент is an animate noun (a living person), its Accusative plural form is identical to its Genitive plural form, which takes the -ов ending.

If I wanted to ask "Did you manage to persuade the clients?", how would the verbs change?

You would change the main verb to the past tense perfective, matching a one-time completed result: Тебе удалось уговорить клиентов? The infinitive уговорить would stay exactly the same.