The source says carrot is not much affected by pests. For nematodes: neem cake 1 t/ha at planting; or a mustard bio-fumigation crop followed by neem cake 250 kg/ha with Purpureocillium lilacinus 5 kg/ha. A leaf-spot spray (chemical) is also listed — ask your officer before using it.
Pending expert review
Source
Crop Production Guide – Horticulture Crops 2020 (Directorate of Horticulture and Plantation Crops, Tamil Nadu & Tamil Nadu Agricultural University (TNAU)), Carrot – Plant protection (nematode), p. 129