Writer takes exam without company in Whitsuntide (9)
I believe the answer is:
pentecost
'whitsuntide' is the definition.
(I've seen this before)
'writer takes exam without company' is the wordplay.
'writer' becomes 'pen' (I've seen this before**).
'takes' means one lot of letters go next to another.
'exam' becomes 'test' ('test' can be a synonym of 'exam').
'without' means one lot of letters goes inside another ('without' can be similar in meaning to 'outside').
'company' becomes 'co' (abbreviation).
'test' going around 'co' is 'tecost'.
'pen'+'tecost'='PENTECOST'
'in' is the link.
(Other definitions for pentecost that I've seen before include "Whitsuntide" , "Christian festival on Whit Sunday" .)