With GNU sed :
sed '2,$ s/[^\t]*\t//' file
Portable :
tab=$(printf '\t')
sed '2,$ s/[^'"$tab"']*'"$tab"'//' file
- 2,$ from the second line to the last line
- s/[^\t]*\t// substitute any character except the tab character to the next tab (the first tab) with nothing.