Sees Mike in second half of winter term at uni (8)
I believe the answer is:
semester
'term at uni' is the definition.
'semester' can be an answer for 'term' (I've seen this in another clue). I am not certain of the 'at uni' bit.
'sees mike in second half of winter' is the wordplay.
'mike' becomes 'M' (phonetic alphabet: alpha, bravo, charlie etc.).
'in' means one lot of letters goes inside another.
'second half of' suggests halving the letters (the back or second half of the word).
'sees' going around 'm' is 'semes'.
'winter' halved is 'ter'.
'semes'+'ter'='SEMESTER'
Can you help me to learn more?
(Other definitions for semester that I've seen before include "Academic period" , "Half year course or term in University" , "Half-year academic course" , "College half-year" , "Half-year division of an academic year" .)