The lucky horse would be joining the county's Mounted Section to help keep the streets of the city safe.
Police have specified that the horse must be aged between 4 and 10, a mare or gelding and at between 15.6hh and 17.3hh.
It also has to be well handled, easy to train and good-natured.
In a statement on Twitter, the WYP horse account said: "West Yorkshire Police are currently looking for a new police horse to buy. The horse would need to fit the following criteria. Between 16.3hh and 17.3hh aged between 4 and 10 years. Mare or gelding. Breeding shire/ Clydesdale/Irish draught or similar.
"Sound, well handled, trainable, good-natured with no vices. Good to shoe, clip and in traffic. No medical issues. Doesn't need to be well schooled but an understanding of walk trot and canter preferable. [The horse] would be vetted and required for a 4-week trial."
Police have asked anyone with enquiries to email [email protected]