replace next line after line match
sed '/^3/{ n; s/.*/x/ }' <(seq 7)
replace second line after line match
sed '/^3/{ n; n; s/.*/x/ }' <(seq 7)
append/insert a new line after match
sed '/^3/a new_line' <(seq 7)
jump 1 line after match and append a new line
sed '/^3/!{ p; d }; n; a new_line' <(seq 7)
jump 2 lines after match and insert a new line
sed '/^3/!{ p; d }; n; n; a new_line' <(seq 7)