Ely desperately after pen to house college transport (7)
I believe the answer is:
bicycle
'transport' is the definition.
(bicycle is a kind of transport)
'ely desperately after pen to house college' is the wordplay.
'desperately' indicates anagramming the letters.
'after' says to put letters next to each other.
'pen' becomes 'bic' (pen manufacturer).
'to house' indicates putting letters inside.
'college' becomes 'c'.
'ely' is an anagram of '[ely]'.
'[ely]' put after 'bic' is 'bic[ely]'.
'bicyle' enclosing 'c' is 'BICYCLE'.
(Other definitions for bicycle that I've seen before include "Pedalled vehicle" , "Two-wheeled transport" , "Lowest values" , "Bike" , "Tour de France racer?" .)