One of the requirements for Inter-Knot Reputation Rank-ups is reaching certain Inter-Knot Levels.
You can earn Inter-Knot EXP by:

• Completing Story Commissions
• Completing battles, explorations, and city commissions in various areas
• Completing HIA Career Club challenges
• Completing other game modes that become available later

More content will become available as your Inter-Knot level rises:

Unlock the level cap of Agents

Unlock more storyline content

Accept more challenging commissions