Short answer

Partly. The Prophet (ﷺ) told men to let the beard grow and to trim the moustache. Islam does not ask a man to cut the hair of his head in daily life. He may wear it long, as the Prophet (ﷺ) did, and he may wear a turban. But Islam does not keep all hair uncut as a vow. Men trim the moustache and nails and remove armpit and pubic hair. At the end of Hajj or Umrah a man shaves his head or shortens his hair. The schools of Islamic law differ on shaving or trimming the beard. So a Sikh who becomes Muslim can keep his beard and his long hair, and wear a turban, in daily life. Islam's answer is that the Creator who gave us our hair also taught, through His last Prophet (ﷺ), how to keep it. And He looks first at the heart.

What Islam asks of a man's hair
HairWhat Islam asksWhen
BeardLet it growIn daily life
MoustacheTrim itIn daily life
Hair of the headKeep it long or cut it, but never shave it in patchesIn daily life
Armpit and pubic hairRemove itIn daily life
Hair of the headShave it or shorten itAt the end of Hajj or Umrah
TurbanMay be wornIn daily life, but not in ihram

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