There might be a problem with your data and you might have duplicate ids on either of your tables. A quick solution could be the following but it might not be the best option.

SELECT appl_no,

id,

per.f_name,

per.l_name,

approved,

credential,

broadening,

getdate() 'sent'

FROM testers t

--Might need OUTER APPLY

CROSS APPLY(select TOP 1 f_name, l_name from person p where p.id = t.id) per