Personal servant's dismal day, running around (5,4)

I believe the answer is:

ladys maid

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'personal servant's' is the definition.
'lady's maid' can be an answer for 'servant's' (lady's maid is a kind of servant). I am unsure of the 'personal' bit.

'dismal day running around' is the wordplay.
'running around' indicates anagramming the letters.
'dismal'+'day'='dismalday'
'dismalday' is an anagram of 'LADYS-MAID'.

Can you help me to learn more?

(Other definitions for ladys maid that I've seen before include "dresser" , "Servant" , "One attending her mistress (mainly historical)" , "Abigail" .)

I've seen this clue in The Times.

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