I have better things to do with my time, like ____ more clients.
This is an example of parallel structure. The infinitive "to do" should match the other option, which should be "to get." I don't mind the second one, or even the first much, but the third is correct.
there are some verbs must be followed by ing form , such as like.
It is not a parallel structure. 'like' here is not a verb, but means the same as 'such as' and is followed by the 'ing' form (here a gerund)
Totally agreed with old gobbo.