Planting bare root whips while a cheap option may not be successful. We are coming out of planting season so container /pot grown may be your only option. Keep in mind If light levels are bad then newly planted whips / feathers can be easily out competed by existing hedging or the ivy. Existing roots shouldn't be too much of a problem given the size you want to plant. Alternatively take out a section and replant with feathers in next planting season. Or If the hedge is mature and in good health it may well fill In over time so no need to fill in at ll. Pictures would help