The Olympic motto, “Faster, Higher, Stronger” stays the same for every Olympics. And of course, the torch -- a symbol of peace, light and friendship -- is always there.

(from an English textbook for junior high school students in China, co-published by DC Canada Education Publishing and Hebei Education Press)

In a symbol of peace, light and friendship, I wonder if that ‘of’ could be replaced with ‘for’.

Many thanks in advance.

 

No, "of" is the correct word, and means "representing". "For", not that it's likely to be used, would suggest "taking the place of".

You could say "standing for" with the same meaning as "of", but I suggest sticking with "of".

 

You can use "for" in other sentences
in mathematics (The symbol for summation is ∑)
in science (the symbol for nitrogen is N)

 

A symbol of peace means it represents peace.
I’ve never heard the wording “symbol for” but I would interpret it to mean “a symbol that tells viewers that you want peace.”