How to get this substring on bash script?

With bash parameter expansion:

$ var='tSA_15_20161014_11-12-50'

$ var="${var#*_}"  ## Extracts the portion after first `_` i.e. 
                      new `var` will be `15_20161014_11-12-50`

$ var="${var#*_}"  ## again gets the portion after first `_`, so in this case
                      after operation `var` will contain `20161014_11-12-50`

$ echo "${var//[-_]/}"  ## Replaces all `-` and `_` from `$var` with null
20161014111250

Given

var='tSA_15_20161014_11-12-50'

then

IFS=_ read -a arr <<< "${var//-/}"
printf '%s%s\n' "${arr[2]}" "${arr[3]}"
20161014111250

For completeness, a few sed versions:

echo "tSA_15_20161014_11-12-50" \
| sed -rn 's/^tSA_[0-9]{1,3}_([0-9]{8})_([0-9]{2})-([0-9]{2})-([0-9]{2})$/\1\2\3\4/p'

echo "tSA_15_20161014_11-12-50" \
| sed -r 's/^tSA_[0-9]{1,3}_([0-9]{8})_([0-9]{2})-([0-9]{2})-([0-9]{2})$/\1\2\3\4/'

echo "tSA_15_20161014_11-12-50" \
| sed -r 's/([^_]*_){2}(.*)_(.*)/\2\3/;s/-//g'

echo "tSA_15_20161014_11-12-50" \
| sed -r 's/(.*_){3}/\1/;s/[-_]//g'

One thing I find important is error checking. In case the variable does not conform exactly to the format you have given, the first version will yield an empty string, and the second version will yield the input string, unchanged. The third version is a sed version of @debal's awk answer, and the fourth is as concise as I can easily get it, both without specified behavior on incorrect input.

Another awk approach. Since awk can take multiple characters as field separators, this can be done in a single step:

$ awk -F'[-_]' '{print $3$4$5$6}' <<<"$var"
20161014111250

Alternatively, in Perl:

$ perl -pe 's/.+?_.+?_//; s/[-_]//g' <<<"$var"
20161014111250

Or

$ perl -F_ -ane 's/-//g for @F; print @F[2..$#F]' <<<"$var"
20161014111250

I'm using here strings, but if your shell doesn't support them just echo $var | command for each command above.

Python solution, using re.split() with multiple tokens. Input string is provided as command line argument

$ python -c 'import sys,re;print("".join(re.split("[-_]",sys.argv[1])[2:]))' "tSA_15_20161014_11-12-50"
20161014111250

Similar approach with ruby:

$ ruby -ne 'puts $_.split(/[-_]/)[2..-1].join("")' <<<  "tSA_15_20161014_11-12-50"                                                   
20161014111250