We report the tentative detection in space of the nitrosylium ion, NO$^+$. The observations were performed towards the cold dense core Barnard 1-b. The identification of the NO$^+$ $J$=2--1 line is supported by new laboratory measurements of NO$^+$ rotational lines up to the $J$=8--7 transition (953207.189,MHz), which leads to an improved set of molecular constants: $B_0 = 59597.1379(62)$,MHz, $D_0 = 169.428(65)$,kHz, and $eQq_0(textrm{N}) = -6.72(15)$,MHz. The profile of the feature assigned to NO$^+$ exhibits two velocity components at 6.5 and 7.5 km s$^{-1}$, with column densities of $1.5 times 10^{12}$ and $6.5times10^{11}$ cm$^{-2}$, respectively. New observations of NO and HNO, also reported here, allow to estimate the following abundance ratios: $X$(NO)/$X$(NO$^+$)$simeq511$, and $X$(HNO)/$X$(NO$^+$)$simeq1$. This latter value provides important constraints on the formation and destruction processes of HNO. The chemistry of NO$^+$ and other related nitrogen-bearing species is investigated by the means of a time-dependent gas phase model which includes an updated chemical network according to recent experimental studies. The predicted abundance for NO$^+$ and NO is found to be consistent with the observations. However, that of HNO relative to NO is too high. No satisfactory chemical paths have been found to explain the observed low abundance of HNO. HSCN and HNCS are also reported here with an abundance ratio of $simeq1$. Finally, we have searched for NNO, NO$_2$, HNNO$^+$, and NNOH$^+$, but only upper limits have been obtained for their column density, except for the latter for which we report a tentative 3-$sigma$ detection.
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