Ralph Maus sent me on an intriguing search, courtesy of Jan Karon, who wrote in her most recent book, Somewhere Safe with Somebody Good, of 2014: “She smiled a little; he saw the light in her eyes. ‘You adimpleate my spirit,’ she said.”
A number of sites online claim to know it but only a couple correctly say that it means to fill up or make complete. It derives from Latin adimplere, to fill up. My best guess is that it’s pronounced as spelled, AD-im-plete.
It’s in the online Oxford English Dictionary, but spelled adimplete. In the 1989 Second Edition it was adimpleate, which is no doubt where Ms Karon found it. The entry was revised in 2011 and the headword changed to adimplete because the two examples which its compilers unearthed, from 1657 and 1778, both spell it without the second a; this matches the Latin past participle adimplet- that is considered to be its direct origin.
The word is justly described as obsolete and rare. Ms Karon seems to be the first person for more than two centuries to use it in print. Her example is so rare that it stands a good chance of being included in the next edition of the OED.