But the one at LSE won’t be the cheapest available! (7,5)

'available' is the definition.
Both the definition and answer are adjectives.
Perhaps you can see an association between them that I don't see?

'but the one at lse won't be the cheapest' is the wordplay.
I cannot really understand how this works, but
'one' could be 'a' and 'a' is found in the answer.
'at' could be 'on' (location) and 'on' is located in the answer.
This may be the basis of clue (or it may be nonsense).