Picking up pet, I become reticent (8)
I believe the answer is:
taciturn
'reticent' is the definition.
('taciturn' can be similar in meaning to 'reticent')
'picking up pet i become' is the wordplay.
I cannot quite see how this works, but
'i' could be 'a' and 'a' is present in the answer.
'become' could be 'turn' ('turn' can be a synonym of 'become') and 'turn' is found in the answer.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for taciturn that I've seen before include "Tending to silence" , "Reticent" , "Untalkative" , "Not inclined to conversation" , "Far from talkative" .)