LinkedIn and a CV can support the same professional story without having the same length. A profile may be broader, while a CV selects facts for an application. Roles, organisations and dates should remain consistent.
Check the public profile before linking to it. Update an old headline and empty descriptions. Do not present someone else's achievements as yours. The link supplements the document, but essential information should remain in the CV. A reader should not need another website to understand your basic work history.
Detailed guide
Writing a CV in English: six checks beyond a literal translation
