Is it always the same ODBC format yyyy-MM-dd? Then this should work:
declare @string varchar(200) = 'Name - Koteswararao vp Department - Prod Location - Hyderabad Domain - ND Job Title - Technical-ABAP Date of Hire - 2021-07-05 Vendor ID - v2345 Candidate ID - Associate ID - 3334 Name - Hardware Allocation';
select substring(@string, PATINDEX('%20[0-9][0-9]-[0-1][0-9]-[0-3][0-9]%', @string), 10)