To keep your hair from getting stuck in a razor you should shave in the direction of the hair growth and rinse the razor frequently.
Also use a good shaving cream or shaving gel when shaving and exfoliate the area before you shave which helps to prevent the hair from getting stuck in the razor.
Shaving in the direction of your hair growth also prevents the hairs from being pushed under your skin and becoming trapped.
And the shaving cream or shaving gel also creates a barrier between the razor and your skin and allows the razor to glide easily and smoothly and reduces friction.
And after each stroke of the razor you should also rinse the razor under some running water which will dislodge any trapped hair or other debris.
Ensure you're using a sharp razor and not a dull razor as dull razors can pull on the hairs being shaved and increase the risk of razor bumps and ingrown hairs.
And avoid pulling on the skin, as this can cause the hairs to be pulled back under your skin and lead to ingrown hairs.
Also moisturize after shaving which helps to keep your skin hydrated and reduce irritation and avoid shaving too closely as well as it can lead to ingrown hairs.
Using an open comb razor and then loosening but not removing the cap to rinse every couple of passes can also help prevent hairs from becoming stuck in the razor.