"To complete the look" means adding or doing something that enhances or finishes the overall appearance or style of something or someone. Full definition
Open shelving opens up the room while keeping dishes organized, and a distressed wall finish completes the look with a charming country feel. (hgtv.com)
Use a deep plum to add depth to eye and then complete the look by adding a brighter color of purple just above the iris. (skincareof.com)
Style these with a maternity blouse and boots for complete look. (shoppinkblush.com)