Somehow brighten outside of university with a climbing plant (10)

'climbing plant' is the definition.
The definition and answer can be both plants as well as being singular nouns.
Maybe they are linked in a way I don't understand?

'somehow brighten outside of university with a' is the wordplay.
I cannot quite understand how this works, but
'university' could be 'u' (abbreviation for university) and 'u' is present in the answer.
an anagram of 'brighten' is 'thnbergi' which is present in the left over letters.
'a' is within the answer.
This accounts for all the letters.
This may be the basis of clue (or it may be nonsense).

Can you help me to learn more?