Second pier ran to part of church (5)
I believe the answer is:
spire
'part of church' is the definition.
'second pier ran' is the wordplay.
'second' becomes 's' (common abbreviation**).
'ran' indicates an anagram (letters have run around).
'pier' is an anagram of 'pire'.
's'+'pire'='SPIRE'
'to' is the link.
(Other definitions for spire that I've seen before include "Tall cone-shaped structure on church" , "Church feature visible from a distance" , "Pointed church tower" , "Church steeple" , "Feature of many churches" .)