A female horse was the first faller (4)

I believe the answer is:

adam

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

'horse was the first faller' is the definition.
I know that 'first' relates to this answer.

'a female' is the wordplay.
'female' becomes 'dam' (dam is a kind of female).
'a'+'dam'='ADAM'

Can you help me to learn more?

(Other definitions for adam that I've seen before include "First person" , "Eves husband" , "Eden inhabitant" , "neoclassical style" , "Eden man" .)

I've seen this clue in the Evening Standard.

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