Koj, Daijs, Nikk
0 n-grams

I think this is closer. Marginal.

@@ -12 +12,2 @@
-<gloss>exchange of diplomatic representatives</gloss>
+<misc>&arch;</misc>
+<gloss>sending a messenger to present gifts</gloss>

daijs
使いをやって安否を問うこと。また、使者を派遣して、贈り物をすること。

Current gloss appears incorrect(see daijs). Term extremely rare.  No ngrams. No news, no twitter, few google, old books.  7 entries on wikipedia all reference the same identical passage:
或屬韓或屬倭，國王不能自通使聘
Example:
https://ja.wikipedia.org/wiki/三韓征伐

Google hits bolstered by this also being Chinese.

Either:
1. redo gloss by trusting daijs and translating the daijs definition
2. delete the entry, because we can't confirm the meaning anyway, because there are almost no accessible examples to look at.

Here's a quick attempt at a new gloss from daijs, but I'm not sure I really understand the definition.
[1] inquiring about someone's wellbeing via envoy. dispatching an envoy to deliver gifts.

We can't have every obscure term. Here's one we are missing that I encountered looking for this one: 
聘問	196 daijs: (スル)進物をたずさえて訪問すること。

Well, there are *some* examples of 使聘 in google books. Here's one...
琉球の若い芸術家は、この時初の内、琉球の使聘事終て帰るとて、伏見に来り止ると聞て、同月八日にかしこに在る薩摩守の第に行向ひて、美里みざと期をあやまりしかば、其の来るを待に不レ及、十月十二日に打立、同廿四日京に入りぬ。

That doesn't really explain what 使聘 means, but it seems consistent with having been dispatched as an envoy...