Keep One's Hair On Meaning

(idiomatic, Britain, colloquial) To stay calm; to be patient.

Example:   All right, all right, just keep your hair on, mate.
1901, Louis Couperus, Alexander Teixeira de Mattos (translator), Small Souls,
  â€œOh, nothing, nothing!”
  â€œYes, there’s something. I mean to know!”
  â€œKeep your hair on; it’s nothing.”
  â€œOut with it!” cried Addie, scarlet with rage.
  And he flew at Jaap’s throat.