Shark or dog taking pee first (9)

I believe the answer is:

porbeagle

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

'shark' is the definition.
(I know that porbeagle is a type of mackerel shark)

'or dog taking pee first' is the wordplay.
'dog' becomes 'beagle' (beagle is a kind of dog).
'taking pee' becomes 'p' (I am not sure about the 'taking' bit.).
'first' says to put letters next to each other.
'or'+'beagle'='orbeagle'
'orbeagle' put after 'p' is 'PORBEAGLE'.

Can you help me to learn more?

(Other definitions for porbeagle that I've seen before include "Shark" , "Swimmer" .)

I've seen this clue in The Sunday Times and The Times.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.