The perfect active of klei/w ("I close, I confine": LSJ entry at web address 1) is first attested in Theophrastus, Characters 18.4 and in the Septuagint (1 Kingdoms 23:20, web address 2), and is not frequent in Greek literature.
The present gloss appears to relate to the Septuagint's usage (LSJ s.v., III.2, "deliver bound"): keklei/kasin au)to\n ei)s ta\s xei=ras tou= basile/ws "they have shut him up into the hands of the king"; NIV: "we will be responsible for handing him over to the king") (However, LSJ s.v. a)sfali/zw records the sense "shut up, close" for Nehemiah 3:15 LXX, and Modern Greek sfalnw= also means "shut".)
Nevertheless [DW] the present entry's first person singular might be quoted from Libanius, Letters 1329.2: ke/kleika toi=s toiou/tois ta\s qu/ras.