Jamieson, Fausset and Brown on Leviticus 21:10-15

10-15. he that is the high priest among his brethren ... shall not uncover his head, nor rend his clothes--The indulgence in the excepted cases of family bereavement, mentioned above [Le 21:2, 3], which was granted to the common priests, was denied to him; for his absence from the sanctuary for the removal of any contracted defilement could not have been dispensed with, neither could he have acted as intercessor for the people, unless ceremonially clean. Moreover, the high dignity of his office demanded a corresponding superiority in personal holiness, and stringent rules were prescribed for the purpose of upholding the suitable dignity of his station and family. The same rules are extended to the families of Christian ministers (1Ti 3:2; Tit 1:6).