Old-fashioned tube going round university's shed (8)
I believe the answer is:
outhouse
'shed' is the definition.
(I've seen this before)
'old-fashioned tube going round university's' is the wordplay.
'old-fashioned' becomes 'out' (as opposed to 'in').
'tube' becomes 'hose' (hose is a kind of tube).
'going round' means one lot of letters goes inside another (some letters go around others).
'university' becomes 'U' (abbreviation as in UMass).
'hose' going around 'u' is 'house'.
'out'+'house'='OUTHOUSE'
(Other definitions for outhouse that I've seen before include "External building" , "Building near home" , "Smaller building separate from main one" , "Construction" , "Building in the grounds of a house" .)