She studies small church with icehouse erected on both sides (10)
I believe the answer is:
schoolgirl
'she studies' is the definition.
'with icehouse erected on both sides' is the wordplay.
'with' indicates putting letters inside.
'icehouse' becomes 'igloo' (house made from ice).
'erected' shows that the letters should be reversed in order.
'on both' becomes 'sch' (I can't explain this - if you can you should give a lot more credence to this answer).
'sides' becomes 'rl' (I've seen this in other clues).
'igloo' in reverse letter order is 'oolgi'.
'sch'+'rl'='schrl'
'oolgi' put within 'schrl' is 'SCHOOLGIRL'.
'small church' is the link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
(Other definitions for schoolgirl that I've seen before include "one found in stream" , "one should learn" , "Female pupil" .)