Short period in school with competition in paved area by building (7)
I believe the answer is:
terrace
'paved area by building' is the definition.
(I've seen this before)
'short period in school with competition' is the wordplay.
'short' means to remove the last letter.
'period in school' becomes 'term' (school term).
'with' says to put letters next to each other.
'competition' becomes 'race' (race is a kind of competition).
'term' with its last letter taken away is 'ter'.
'ter'+'race'='TERRACE'
'in' is the link.
(Other definitions for terrace that I've seen before include "Stadium standing area" , "From which spectators watch" , "Abutting row of houses" , "Balcony" , "Stadium's standing area" .)