Can I get admission in the second year of B.Tech. in computer science?

No, lateral entry, or direct second-year admission, is not available at NIT Agartala for B.Tech computer science or any other subject. Like all other NITs, NIT Agartala only admits students for the first year of B.Tech through JEE Main and then JoSAA counselling.
NITs do not offer lateral entry (after diploma). The facility is typically available at private and state-level colleges, but not at NITs or other central government institutions.
Colleges like Tripura Institute of Technology (TIT), Agartala, which offers lateral entry B.Tech after diploma, or any state technical university that accepts lateral entry through LEET or state-level entrance exams are options for diploma holders.
For more details, you can check out Collegedunia’s Page