this Administration calendar entry confirms the connection -
Deceased : William Henry Clapp
Primary Beneficiary/Executor : William Henry Bant Clapp
Date of Death : 18 Mar 1868
County of Death : Cork
9th Apr 1868, Letters of Administration of the personal estate of William Henry Clapp late of Waterloo place, Cork Esq. deceased, who died 18 March 1868 granted at Cork to William Henry Bant Clapp of Milton Barracks, Gravesend, England, Medical Doctor the son and universal legatee.
see :
link (Will calendars National Archive of Ireland)