We present new VLA observations at 1.4 GHz confirming the presence of a radio halo at the centre of the cluster A3562 , in the core of the Shapley Concentration . We also report a detailed multifrequency radio study of the head tail galaxy J1333–3141 , which is completely embedded in the halo emission . The radio halo has an irregular shape , and a largest linear size of \sim 620 kpc , which is among the smallest found in the literature . The source has a steep spectrum , i.e . \alpha _ { 843 ~ { } MHz } ^ { 1.4 ~ { } GHz } \sim 2 , and its total radio power , P _ { 1.4 ~ { } GHz } \sim 2 ~ { } \times 10 ^ { 23 } W Hz ^ { -1 } , is the lowest known to date . The radio power of the halo and the X–ray parameters of the cluster , such as L _ { X } and kT , nicely fit the correlations found in the literature for the other halo clusters , extending them to low radio powers . We found that the total number of electrons injected in the cluster environment by the head–tail source is enough to feed the halo , if we assume that the galaxy has been radio active over a large fraction of its crossing time . We discuss possible origins of the radio halo in the light of the two–phase model ( Brunetti et al . 2001 ) and propose that the observed scenario is the result of a young source at the beginning of the reacceleration phase .