Cochlear Implants (CIs) enhance linguistic skills in deaf or hard of hearing children (D/HH). However, the benefits of CIs have not been sufficiently studied, especially with regard to communicative-pragmatics, i.e., the ability to communicate appropriately in a specific context using different expressive means, such as language and extralinguistic or paralinguistic cues. The study aimed to assess the development of communicative-pragmatic ability, through the Assessment Battery for Communication (ABaCo), in school-aged children with CIs, to compare their performance to a group of children with typical auditory development (TA), and to investigate if CI received under the age of 24 months promotes the typical development of such ability. Results show that children with CIs performed significantly worse than TA on the paralinguistic and contextual scales of the ABaCo. Finally, the age of first implantation had a significant role in the development of communicative-pragmatic ability.