Mammal and steed both sea-sick (9,3)

I believe the answer is:

horseshoe bat

'mammal' is the definition.
(horseshoe bat is a kind of mammal)

'steed both sea-sick' is the wordplay.
'steed' becomes 'horse ' (I've seen this in another clue).
'sick' indicates an anagram.
'both'+'sea'='bothsea'
'bothsea' with letters rearranged gives 'shoebat'.
'horse'+'shoebat'='HORSESHOE BAT'

'and' is the link.

(Another definition for horseshoe bat that I've seen is " Insectivorous mammal".)

I've seen this clue in The Guardian.

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