Determined chap squeezed inside, a bit taken aback (7)
I believe the answer is:
adamant
'determined chap' is the definition.
'adamant' can be an answer for 'determined' (I've seen this before). I am unsure of the 'chap' bit.
'squeezed inside a bit taken aback' is the wordplay.
'squeezed' becomes 'man' (I am not sure about this - if you are sure you should believe this answer much more).
'inside' is an insertion indicator.
'bit' becomes 'tad' (both can mean a small amount).
'taken aback' says the letters should be written in reverse.
'tad' reversed gives 'dat'.
'a'+'dat'='adat'
'man' put within 'adat' is 'ADAMANT'.
Can you help me to learn more?
(Other definitions for adamant that I've seen before include "With mind made up" , "Legendary rock" , "Impervious to pleas or persuasion" , "Data man can be quite unyielding" , "Positive and unrelenting" .)