See hospital about to admit sick and “peaky” types (8)

I believe the answer is:

hilltops

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'peaky types' is the definition.
Although both the answer and definition are plural nouns, I don't see how they can define each other.

'see hospital about to admit sick' is the wordplay.
'see' becomes 'spot' (to spot is to notice or catch sight of).
'hospital' becomes 'h' (abbreviation for hospital on maps).
'about' is a reversal indicator.
'to admit' indicates putting letters inside.
'sick' becomes 'ill' (synonyms).
'spot'+'h'='spoth'
'spoth' in reverse letter order is 'htops'.
'htops' placed around 'ill' is 'HILLTOPS'.

'and' acts as a link.

Can you help me to learn more?

I've seen this clue in The Times.

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