If you want admission in that college for engineering or science then you do not need NEET exam because NEET is only for medical courses like MBBS BDS or BAMS. For engineering branches like ECE or other degrees you need entrance like JEE Main or state exam like TNEA or KCET depending on your state. If the college is engineering college in Coimbatore then you apply through TNEA counselling or JEE Main and do choice filling. If the college is for medical or physiotherapy then you must use NEET score. So you will need to check which course you want and then see which entrance exam applies. Entrance exam and university counselling is main path for admission without NEET.

And if it is a medical allied health or other professional course you must check NEET eligibility and counselling after NEET exam

https://medicine.careers360.com/articles/neet-eligibility-criteria