Period of British rule concerning Cyprus -- see information inside (7)
I believe the answer is:
regency
'period of british rule' is the definition.
(period of English history 1811-1820)
'concerning cyprus see information inside' is the wordplay.
'concerning' becomes 're' (both can mean on a particular topic).
'cyprus' becomes 'cy' (abbreviation).
'see information' becomes 'gen' (gen can informally mean information).
'inside' indicates putting letters inside.
're'+'cy'='recy'
'recy' enclosing 'gen' is 'REGENCY'.
(Other definitions for regency that I've seen before include "Late eighteenth century to early nineteenth century style" , "Period 1811-1820 in UK" , "Periods of the Madness of King George when the Prince of Wales took over" , "Period (1811-20) covering The Madness of King George III" , "Period of king's incapacity" .)