Name of church improved taking time (8)
I believe the answer is:
christen
'name' is the definition.
'church improved taking time' is the wordplay.
'church' becomes 'ch' (common abbreviation).
'improved' becomes 'risen' (as in figures rising in a chart).
'taking' indicates putting letters inside.
'time' becomes 't'.
'risen' going around 't' is 'risten'.
'ch'+'risten'='CHRISTEN'
'of' acts as a link.
(Other definitions for christen that I've seen before include "Use for the first time" , "Baptise and name" , "Give a name to (baby)" , "attach handle to" , "Name in church" .)