Do changes in interest rates affect all market bond prices or only the newly issued ones?

All, imagine holding a 4% interest rate bond from ABC Co. or buying a newly launched 4% interest rate bond from ABC Co.. When interest rates go up from e.g. 2% to 3% (meaning you could get a govt bond at 3% now instead of 2%), that 4% interest rate bond from ABC Co. doesn't look as attractive anymore.

Hence, when interest rates go up, private companies will have to borrow money at a higher rate and hence bond launch after the interest rate increase will be of higher interest rates, vice versa.