On 20 August 2015, Palmiero was signed by Serie C side Paganese on a season-long loan deal. On 20 September e made his Serie C debut for Paganese as a substitute replacing Emanuele Cicirelli in the 93rd minute of a 2–1 home win over Fidelis Andria. On 5 December he played his first entire match for Paganese, a 2–1 away defeat against Matera. On 24 January 2016, Palmiero scored his first professional goal in the 42nd minute of a 3–1 home win over Martina Franca. On 23 March he scored his second goal, as a substitute, in the 93rd minute of a 2–0 away win over Ischia. Palmiero ended his season-long loan to Paganese with 14 appearances and 2 goals, all in Serie C.
On 1 July 2016, Palmiero was loaned to Serie C side Akragas on a season-long loan deal. On 30 October he made his Serie C debut for Akragas as a substitute replacing German Cochis in the 63rd minute of a 3–1 away defeat against Matera. On 27 November, Palmiero played his first match as a starter for Akragas, a 2–0 away defeat against Paganese, he was replaced by Matteo Zanini in the 60th minute. On 3 December he played his first entire match for Akragas, a 1–0 away win over Casertana. On 30 April 2017 he received a red card in the 55th minute of a 3–1 home defeat against Juve Stabia. Palmiero ended his loan to Akragas with 25 appearances, 21 as a starter and 3 assists, all in Serie C.
On 18 July 2017, Palmiero with Gennaro Tutino and Luigi Liguori were signed by Serie C side Cosenza on a season-long loan deal. On 30 July he made his debut for Cosenza, as a starter, in a 3–2 home defeat, after extra-time, against Alessandria in the first round of Coppa Italia, he was replaced by Massimo Loviso in the 63rd minute. On 9 September, Palmiero made his Serie C debut for Cosenza as a starter in a 0–0 away draw against Matera, he was replaced by Matteo Calamai in the 56th minute. On 3 December he played his first entire match for Cosenza, a 0–0 awat draw against Rende. On 11 February 2018, Palmiero scored his first goal for Cosenza in the 26th minute of a 2–2 away draw against Catania. Palmiero ended his loan to Cosenza with 36 appearances, 1 goal and he helped Cosenza to reach the promotion in Serie B. On 24 July 2018, Palmiero returned to Cosenza with a new season-long loan. On 4 August he started his second season with Cosenza in a 2–1 away win, after extra-time, over Trapani in the second round of Coppa Italia, he played the entire match. On 12 August he played in the third round in a 4–0 away defeat against Torino. On 27 August he made his Serie B debut as a substitute replacing Riccardo Maniero in the 60th minute of a 1–1 away draw against Ascoli. On 30 September he played his first entire match of the season, in Serie B, a 1–1 home draw against Perugia. On 5 May 2019, Palmiero scored his first goal of the season in the 90th minute of a 2–1 away win over Salernitana. Palmiero ended his second season on loan at Cosenza with 30 appearances, 1 goal and 1 assist.
Loan to Pescara
On 23 July 2019, Palmieri joined Serie B side Pescara on loan until 30 June 2020. On 11 August he made his debut for the club in a 3–2 home win against Mantova in the second round of Coppa Italia, he played the entire match. On 1 September he made his league debut and he scored his first goal for the club in the 94th minute of a 4–2 home win over Pordenone, he played the full match.
International career
Palmiero represented Italy at Under-16, Under-17 and Under-18 level and he collected a total of 18 caps. On 10 April 2012, Palmiero made his debut at U-16 level as a substitute replacing Jose Mauri in the 51st minute of a 2–0 away win over Scotland U-16. On 19 December 2012, Palmieri made his debut at Under-17 level as a starter in a 1–0 away defeat against Greece U-17, he was replaced by Mario Pugliese in the 30th minute. On 21 February 2013 he played his first entire match for Italy U-17, a 3–3 away draw against Turkey U-17. On 14 August 2013 he made his first and only appearances for Italy U-18 as a substitute replacing Gennaro Tutino in the 56th minute of a 2–1 home defeat against Austria U-18.
