Don't try it. There are various cut-off points between Wy and RHB, and some pretty high cliffs, any one of which can stymie you.
For just the bit "under" the Abbey you could try walking to the end of the bit of beach and see how long before the next high tide (see tide tables available on line or at local angling shops), then allow a bit less to get back. Such a method is only to be attempted under calm conditions, and is not reccommended. Good footwear essential.
On the whole, treat the waterside east of Whitby with EXTREME caution.