앞으로 = To the front --> in the future 도 = also 잘 = well, often 부탁 = request, ask someone to help 드립니다 = give => 앞으로도 잘 부탁드립니다 = In the future, I will also ask for your help. (So please help me in the future)

It can not be translated literally. it would be weird you'd better translate to be more natually with English like "I am looking forward to ~ ( working with you / mee you again) "