Tea leading pair of Cypriots served outside simple priest’s office (10)
I believe the answer is:
chaplaincy
'priest's office' is the definition.
'chaplaincy' can be an answer for 'office' (chaplaincy is a kind of office). I'm not certain of the 'priest's' bit.
'tea leading pair of cypriots served outside simple' is the wordplay.
'tea' becomes 'cha' (cha is a type of tea).
'leading' means one lot of letters go next to another.
'pair of cypriots' becomes 'cy' (I can't explain this - if you can you should give a lot more credence to this answer).
'served outside' is an insertion indicator.
'simple' becomes 'plain' ('plain' can be a synonym of 'simple').
'cha'+'cy'='chacy'
'chacy' going around 'plain' is 'CHAPLAINCY'.
(Other definitions for chaplaincy that I've seen before include "ministerial post" , "Clerical office" , "Religious organisation" , "cleric's office" , "Where ministers are" .)