Is DNA replication required for Protein Synthesis or can proteins be synthesized without DNA being replicated?
DNA replication and protein synthesis are very very different processes. The key thing to remember about protein synthesis is that DNA is not directly used; RNA is. When DNA is replicated, it is for reproduction. When it is transcribed, it is copied, with certain changes, into RNA instead. RNA is then "read" by protein synthesis machinery to produce the proteins.
To directly answer your question, no, replication is not required. If you inject some RNA which codes for a protein into a cell, it will be translated into a protein. There are many viruses which exclusively use RNA for their genetic makeup. The RNA is replicated at some point by the host cell's machinery but the RNA can be directly translated into a protein by the host cell as soon as the RNA enters the cell.
If you have a file on your computer hard drive, a document, and you want to translate that document into a different language, do you need to make a copy of the original file before you translate it?
Making a copy of a file is duplicating it, like replicating the DNA in a chromosome. Translating the document into a different language is “sort of” like translating a messenger RNA into a protein.