mdfdefinestyle{MyFrame}{%
    linecolor=black,
    outerlinewidth=2pt,
    %roundcorner=20pt,
    innertopmargin=4pt,
    innerbottommargin=4pt,
    innerrightmargin=4pt,
    innerleftmargin=4pt,
        leftmargin = 4pt,
        rightmargin = 4pt
    %backgroundcolor=gray!50!white}
        }

% text
begin{mdframed}[style=MyFrame,nobreak=true]
begin{center}
textbf{THIS TEXT SHOULD BE MORE TIGHTLY FRAMED }
end{center}
end{mdframed}

% sipka
begin{figure}[h!]
centering
includegraphics[width=.1textwidth]{sipka3.pdf}
end{figure}
% arrow
begin{mdframed}[style=MyFrame,nobreak=true]
lipsum[2]
end{mdframed}

% sipka
begin{figure}[h!]
centering
includegraphics[width=.1textwidth]{sipka3.pdf}
end{figure}
% arrow
begin{mdframed}[style=MyFrame,nobreak=true]
lipsum[1]
end{mdframed}

documentclass{article}
usepackage{mdframed,lipsum}
begin{document}
mdfdefinestyle{MyFrame}{%
    linecolor=black,
    outerlinewidth=2pt,
    %roundcorner=20pt,
    innertopmargin=4pt,
    innerbottommargin=4pt,
    innerrightmargin=4pt,
    innerleftmargin=4pt,
        leftmargin = 4pt,
        rightmargin = 4pt
    %backgroundcolor=gray!50!white}
        }

% text
lipsum[1]
begin{mdframed}[style=MyFrame,nobreak=true,align=center,userdefinedwidth=30em]
textbf{THIS TEXT SHOULD BE MORE TIGHTLY FRAMED}
end{mdframed}
lipsum[2]
end{document}

documentclass{article}
usepackage{mdframed,lipsum,calc}
begin{document}
mdfdefinestyle{MyFrame}{%
    linecolor=black,
    outerlinewidth=2pt,
    %roundcorner=20pt,
    innertopmargin=4pt,
    innerbottommargin=4pt,
    innerrightmargin=4pt,
    innerleftmargin=4pt,
        leftmargin = 4pt,
        rightmargin = 4pt
    %backgroundcolor=gray!50!white}
        }

newcommandheader[1]{
  newlength{headerwidth}
  setlength{headerwidth}{widthof{#1}}
  addtolength{headerwidth}{8pt}
  begin{mdframed}[style=MyFrame,nobreak=true,align=center,userdefinedwidth=headerwidth]
    #1
  end{mdframed}
}


% text
lipsum[1]
header{textbf{THIS TEXT SHOULD BE MORE TIGHTLY FRAMED}}
lipsum[2]
end{document}