According to the OED definition, it is a local/regional word that means the same as clow. There is only one attestation quoted, from Somerset:
1882 Spectator 6 May 595. In the Reports of the Somerset Drainage Commissioners, the sluices and locks under their jurisdiction are called ‘Clyses’.
Obviously, clow is not exactly a common word, either, but it does seem to be more common than clyse, with about thirty or forty attestations in two meanings (actually three, but one is noted as being obsolete and has a question mark, but no attestations—so slightly paraphrasing the entry numbers here):
A sluice or floodgate: ‘esp. (a) The outfall sluice of a river or drain communicating with a tidal river and provided with flood-gates’. (b) ‘A shuttle in the gates or masonry of a lock, which is raised to admit or discharge water; a similar arrangement by which the admission of water to the wheels of water-mills is regulated’. Peacock Gloss. Manley and Corringham (N. W. Lincoln).
A sluice or sliding door for other purposes.
So a clyse would appear to be just a regional Somerset word for a sluice, basically.
It seems that clow is a false singular, based on an earlier form clowes/clowis. This was originally a singular itself (from Old English clūse, meaning ‘enclosure’, and related to ‘close’, both from the nominalised Latin passive participle clausa ‘closed’, from the verb claudō ‘to close’), but was reinterpreted as clow + plural -es around the 15th or 16th century.
Clyse is less certain: it appears to be from French écluse (same word as the Old English cluse), or perhaps it just represents a dialectical nonce rounding of the u in the Old English, yielding regional *clȳse as a variant of clūse.