Said to have remained sober (5)

I believe the answer is:

staid

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'sober' is the definition.
(synonyms)

'said to have remained' is the wordplay.
'to have' is an insertion indicator.
'remained' becomes 't' (I am not sure about this - if you are sure you should believe this answer much more).
'said' enclosing 't' is 'STAID'.

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(Other definitions for staid that I've seen before include "Very conventional and dull" , "Proper; sedate" , "Serious or sober in character" , "Stuffy, traditional" , "Sedate, unadventurous" .)

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

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