Crossword Genius

Make up the deficiency with a denture perhaps (5,3,3)

Ross

I believe the answer is:

close the gap

I'm a little stuck... Click here to teach me more about this clue!

'make up' is the definition.
I know nothing about this answer so I cannot judge whether it can be defined by this definition.

'the deficiency with a denture perhaps' is the wordplay.
I cannot quite understand how this works, but
an anagram of 'the' is 'eth' which is present in the answer.
'deficiency' could be 'gap' (I've seen this in another clue) and 'gap' is located in the answer.
The remaining letters 'close' is a valid word which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for close the gap that I've seen before include "remedy deficiency" , "Supply what is lacking" .)

I've seen this clue in The Globe and Mail.
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