Mull it over in berth, becoming a little puzzled (7)
I believe the answer is:
bemused
'puzzled' is the definition.
(being bemused is being puzzled or confused)
'mull it over in berth' is the wordplay.
'mull' becomes 'muse' (synonyms).
'it' becomes 'e' ('e' can mean 'electronic' which is similar to 'IT').
'over' is a charade indicator (letters next to each other) (in a down clue, some letters go over others).
'in' means one lot of letters goes inside another.
'berth' becomes 'bd' (I can't justify this - if you can you should give a lot more credence to this answer).
'muse' after 'e' is 'emuse'.
'emuse' placed into 'bd' is 'BEMUSED'.
'becoming a little' is the link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for bemused that I've seen before include "Floored" , "Puzzled" , "Deep in thought" , "Lost for words" , "Perplexed or absorbed in thought" .)