Turns over page, with thick digits, perhaps? (6)
I believe the answer is:
thumbs
'turns' is the definition.
The definition and answer can be both to do with contact as well as being verbs in their -s form.
Maybe there's a link between them I don't understand?
I can't explain the remainder of the clue.
Can you help me to learn more?
(Other definitions for thumbs that I've seen before include "Short thick digits" , "Hitches a lift" , "reads intensively" , "Digits; requests (lift)" , "To be all these is to be clumsy" .)