Saying prayers initially, wanderer heading for basilica (7)
I believe the answer is:
proverb
'saying' is the definition.
(proverb is a kind of saying)
'prayers initially wanderer heading for basilica' is the wordplay.
'initially' says to take the initial letters.
'wanderer' becomes 'rover' ('rover' can be a synonym of 'wanderer').
'heading for' says to take the initial letters.
The first letter of 'prayers' is 'p'.
The initial letter of 'basilica' is 'b'.
'p'+'rover'+'b'='PROVERB'
(Other definitions for proverb that I've seen before include "Saying of great truth" , "Generally true saying" , "Make haste slowly, perhaps" , "Well-known statement incorporating general truth" , "'Adage, saw (7)'" .)