A somewhat old-fashioned, masculine-sounding imperative suffix attached to the -masu stem of a verb. Used mainly by male speakers in formal or authoritative contexts, often in writing or period speech.
See also: 給う
ここに名前を書きたまえ。
Please write your name here.
遠慮なく言いたまえ。
Please speak without reserve.
給う is the base verb meaning 'to give' (honorific). たまえ is derived from its imperative form and used as a suffix.
Derived from the imperative form of the honorific verb 給う (たまう, 'to give'). The suffix usage developed as a polite but authoritative way to request an action.