Unfeeling designates swallow up Open University (7)
I believe the answer is:
callous
'unfeeling' is the definition.
(synonyms)
'designates swallow up open university' is the wordplay.
'designates' becomes 'calls' (I can't justify this - if you can you should give a lot more credence to this answer).
'swallow up' indicates putting letters inside.
'open university' becomes 'OU'.
'calls' placed around 'ou' is 'CALLOUS'.
Can you help me to learn more?
(Other definitions for callous that I've seen before include "Insensitive, cruel" , "Not feeling" , "Hard-hearted" , "Heartless" , "Emotionally hardened" .)