Originally coming from the う-Verb 給（たま）う 'to give', or 'to bestow', the imperative form たまえ
may be seen attached to the ます-stem of verbs, in order to create a light order. It is often translated simply as 'please do (A)'.
Despite this, たまえ
is a structure that is only used to someone of lower status than the speaker, and primarily only by men. This 'lower status relationship' is usually one that is obvious between both the speaker and the listener, such as a boss and subordinate.
Well, please, take a seat.
You look like you want to say something! Please say what you are thinking!
Please eat as much as you want without hesitation.
Fun-fact - In the past, たまえ was sometimes used to ask for favors or for wishes to be granted in prayers. However, this use will primarily only be seen in books in the modern era.